Upgrading house wiring

My house was built in 1950. The electrical wiring has a few fixable problems (no GFCIs, outdoor outlets using indoor receptacles, no grounding, switches in inconvenient places, circuits no longer to code, too few outlets, etc.) but the main problem is that some of the breakers trip due to too much load. I guess in the 1950's they didn't have PCs, flat screen TVs, pot lights, microwaves, etc. So I have a big job of correcting and upgrading the wiring but I am going about it slowly in priority order (safety first then convenience).

My problem now is that I have reached the point where I need to upgrade a 15A circuit to 20A but I am finding it difficult to run my cable the last 1-2 feet to the breakers (is this called an MCB?). The MCB is located in the garage, the cables run down the wall under the house and enter the basement. I can see the cables as they go into the garage floor and again when they enter the basement - the bit inbetween is not visible.

What I am trying to find out is what happens inbetween. Does anyone know when the MCB is in the garage how the cables are brought into the house? Should I be able to run new cable through this area? Or should I create a new channel into the garage (if that is possible)? I will be replacing several cables eventually. I have disconnected the 15A circuit from the breaker and thought I could use this to pull a new 20A cable through but although I have removed all the cable clips that I can see there must be one or two in the area I can't access/see.

Thanks. No - there is no wall board, drywall, etc. to pull off. Nearly all the cables leave the garage panel and go under the garage floor and enter the house through the basement ceiling. There is a 1-2 foot area which is inaccessible being the area where the joists end and presumably the concrete floor of the garage starts. It seems to be a "channel" designed specifically for the purpose of running the cables.

I suppose I could dig up the concrete floor in the garage or try to get to the panel by going through the stud wall above and then into the garage but what I am trying to find out is how this cabling is done so that I choose the best method of replacing the old cables. I am hoping someone with experience of a garage panel can advise.

My guess is that there is a joist at the rim of the house, outside the basement wall, where all the cables are attached. There are about 12 cables within a 2 foot space which would seem to be a derating issue?

I don't have a digital camera. The garage is attached to the house so the wall the panel is on in the garage is the other side of a bedroom wall. The panel is 100A with around 18 Siemens breakers (mostly 15A). It looks like the panel is much newer than the cabling and a couple of the breakers have newer wiring (or pigtail new wire onto the old).

The cables in the basement run under or through the rim joist but I can't see (or photograph what happens after that). The bedroom wall is presumably above this joist.

The cables beneath the panel disappear into the floor. I've removed a wooden board which the cables were fixed to as they went down the wall to the floor and can see the hole in the floor a little better - it's about 2 inches wide and 12 inches long with 15 cables, all unshielded except for one (which is no longer used as it was for an electric water tank). Half of the cables disappear towards the basement - one of these (the shielded cable is movable from each end - so maybe I could use this to pull through new cable?). The first 6 cables seem to go under the concrete floor (one seems embedded in the concrete) but they must turn back towards the basement. Why they are all so tightly packed seems crazy to me - would this pass inspection today?

Sorry, I know a picture would make a world of difference but I'm not sure I could get a decent picture even if I had a camera.

I am half tempted to remove the panel and relocate it to the basement! Would this be a big job? Presumably I would need some conduit for the main hydro line.